Centralizers And Derivations On Reflexive Algebras And Triangular Algebras

In this thesis, we mainly study centralizers, derivations on reflexive algebras and triangular algebras. The thesis consists of four chapters.In Chapter 1, we introduce some terminology and notation, and summarize the background. Also, we state the main results of this thesis.In Chapter 2, the form of commuting map on reflexive algebras is described. Let L be a subspace lattice on Banach space X , then every commuting mapδis of the formδ( A) = TA + h ( A), where T lies in the center of the algebra and h is a linear map from the algebra to its center.In Chapter 3, we studies Jordan centralizers and Jordan derivations on triangular algebras.We prove that every Jordan centralizer is a centralizer, and every Jordan derivation is a derivation. In Chapter 4, we studies the linear map Lie derivable at zero point and respectively, derivable at zero point on CDC algebras. We prove that each linear map Lie derivable at zero point can be uniquely decomposed into the sum of a derivation and a linear mapping with image in the center of the algebra; and ifδbe a continuous linear map derivable at zero point, thenδ( A) = d ( A) +δ( I )A, where d is a derivation.